By Okonek Ch.
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Additional info for 3-Mannigfaltigkeiten im P5 und ihre zugehorigen Stabilen Garben
1 to each p. 2 to the right side (because there are two), and the equality would no longer hold. Of course this would not necessarily change our decision. , movie, vs. picnic) might win. But it might not, because the calculated EU of picnic might increase. The only way to avoid such effects of arbitrary subdivision is to require that the addition rule apply to the weights used to multiply the states. Now consider the multiplication rule. This relates to a different kind of invariance. Our choices should not be affected if we narrow down the space of possibilities to what matters.
But it does violate the addition rule: in general p 2 + q 2 ≠ (p + q)2. Addition of a constant violates both rules. ” Probabilities that seem not to be conditional are simply conditional on your current beliefs. The change from the perspective of the original decision maker to that of the person at point A simply involves a narrowing of the frame of reference. Again, this should not affect the relative goodness of the two options. For details, see Broome (1991), particularly, pp. 68, 69, and 202.
So all these differences are equal in terms of good. In this case, you ought to be indifferent in Choice 4, too. This kind of “tradeoff consistency,” in which Choices 1–3 imply the result of Choice 4, plus a couple of other much simpler principles, implies expected-utility theory. In particular, you can use one of the differences, like the 100–210 difference in B, as a measuring rod, to measure off equal intervals under A. Each of these differences represents the same utility difference. Note that this is all we need.
3-Mannigfaltigkeiten im P5 und ihre zugehorigen Stabilen Garben by Okonek Ch.